Theorem niabn 566

Description: Miscellaneous inference relating falsehoods.

Hypothesis

Ref	Expression
niabn.1	⊢ φ

Assertion

Ref	Expression
niabn	⊢ (¬ ψ → ((χ ∧ ψ) ↔ ¬ φ))

Proof of Theorem niabn

Step	Hyp	Ref	Expression
1		pm3.27 260	. 2 ⊢ ((χ ∧ ψ) → ψ)
2		niabn.1	. . 3 ⊢ φ
3	2	pm2.21ni 92	. 2 ⊢ (¬ φ → ψ)
4	1, 3	pm5.21ni 503	1 ⊢ (¬ ψ → ((χ ∧ ψ) ↔ ¬ φ))

Syntax hints:  ¬ wn 1   → wi 2   ↔ wb 127   ∧ wa 196

This theorem is referenced by:  ninba 575

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-an 198

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